DISTRIBUTION OF
FRACTURE TRANSMISSIVITYIN THE CONGLOMERATE AND SANDSTONEAQUIFERS OF THE SOUTHEASTERN
VOLTAIANBASIN, EAST-CENTRAL GHANA, AFRICA

William M. Turner, Ph.D.

INTRODUCTION

AGW scientists have long been interested in the statistical distribution of aquifer
transmissivity because it is of significant importance in the exploration for ground-water
resources.

Over the past three decade the Word Vision ground-water program in Ghana has produced mixed
results (Acheampong and Hess, 1998).

The high failure rates in drilling successful wells and the high variability of well
yield (World Vision, 1993; Prakla Seismos, 1984) show the need for precise ground-water
exploration methods. Many studies have focused on the hydrogeologic and tectonic
processes. Instead it must be recognized that regardless of the processes leading to
fractures and fracture densities, an understanding of process will not describe the
spatial distribution of aquifer transmissivity. Nor, will it indicate which fracture
contains water.

This paper is based on transmissivity values presented by Acheampong
and Hess (1998). The work reported on by these workers is the outcome of rural water
development program carried out by World Vision in Ghana. Figure
1 shows the area of investigation carried out by Acheampong and Hess (1998).

Acheampong and Hess (1998) did not address either the statistical distribution of
transmissivity or, more importantly, its spatial distribution.

Ground-water flow is through fracture zones to intermittent stream channels and
ultimately to Lake Volta.

The hydrogeology of the area is primarily controlled by secondary porosity in the form
of fractures developed in sedimentary rocks. Primary porosity has been destroyed
through compaction and slight metamorphism.

PROCEDURE

Acheampong and Hess (1998) present 12 transmissivity values for the Conglomerate and 14
values for Sandstone. Of these values, two values are indicated as both Sandstone
and Conglomerate. They are used to enrich both data sets for the purpose of
statistical analysis.

The data set is heavily biased because only data from wells that produced more than 10
liters per minute (l/m) were used.

SANDSTONE

Acheampong and Hess (1998) indicate that the success rate of wells with yields of at
least 10 l/m drilled in the Sandstone ranges from 53 to 66 percent . If the average
success rate is 59.5 percent, the average failure rate is 41.5 percent.

For the purpose of analysis, we assumed that the 14 transmissivity values for wells in
the Sandstone represent the 59.5 percent of the wells that were successful.
Therefore, there were 24 wells in the Sandstone. One of these wells must have had a
transmissivity value such that 100 percent of the wells encountered the aquifer with
higher transmissivities. For purposes of computation, we assumed that there was one
well with a transmissivity of "0" m2/d. This well is ranked
first in Table 1. Table 1 shows the transmissivity values for
the Voltaian Sandstone.

The first value in the table for Sandstone wells is ranked 11 because there were 10
unsuccessful wells in the population of values that had lower transmissivities.

CONGLOMERATE

Acheampong and Hess (1998), for wells drilled in the Conglomerate indicate the success
rate ranges from 38 to 57 percent. If the average success rate is 47.5 percent, the
average failure rate is 52.5 percent. Low capacity wells were not tested. Table 2 contains the data for the wells used in our analysis of
the transmissivity distribution in the Conglomerate.

The 12 transmissivity values for the Conglomerate represent 47.5 percent of the wells
that were successful. Therefore, 25 wells were drilled one of which, we assumed,
encountered an aquifer with a transmissivity of "0" m2/d. The
first well in the table of Conglomerate wells is ranked 14 because there were 13 wells
that had transmissivities less than the first recorded one.

RESULTS

We ranked the classed data and plotted it using the Weibull plotting position method
where p = i/(n+1).

The data is heavily biased because only successful wells were tested. Also, wells
may not have completely penetrated the water-bearing zone and the aquifer performance
tests did not consider wellbore storage effect.

The Weibull plotting position equals the average exceedance probability of the ranked
observations. They are unbiased plotting positions. The data for the Sandstone
and Conglomerate wells are plotted in Figures 2 and 3.

We used the Kolmogorov-Smirnov (Cheeney, 1983) to test whether the frequency
distribution of the transmissivity values is lognormal. The K-S method is an exact
method and is useful when dealing with only a few data points. We have only 14
transmissivity values for Sandstone wells and 12 transmissivity values for Conglomerate
wells.

The maximum absolute deviations between the observed and
calculated transmissivity values for Sandstone and Conglomerate wells were 0.0379 and
0.0627 respectively. These values are far less than the critical "a"
values at the 0.05 significance level of 0.349 and 0.375 for sample sizes of 14 and 12
transmissivity values. The null hypothesis is not rejected and the transmissivity
data can be regarded as coming from a lognormally distributed population.

CONCLUSIONS

The average transmissivity of fractures in Conglomerate wells is about 24.2 m2/d.
The average transmissivity of fractures in Sandstone wells is about 10.8 m2/d.
Fractures in the Conglomerate have greater transmissivity than those in the
Sandstone. Consequently, the Conglomerate terrane of southeastern Ghana is more
prospective for ground water.

The average transmissivity of successful Conglomerate wells is about 24.2 m2/d.
About 78 percent of wells drilled with the best exploration methods including satellite
imagery and aerial photography failed to encounter a fracture with greater than the
average transmissivity. About 50 percent of the wells encountered fractures in the
Conglomerate with less than 1.6 m2/d.

The average transmissivity of successful Sandstone wells is about 10.8 m2/d.
About 80 percent of wells drilled with the best exploration methods including satellite
imagery and aerial photography failed to encountered a fracture with greater than the
average transmissivity. About 50 percent of the wells encountered fractures in the
Sandstone with a transmissivity of less than 1.6 m2/d.

The lowest transmissivity associated with an acceptable well producing 13 l/min is 1.59
m2/d. Using present exploration methods, about 80 percent of the wells
will not meet minimum acceptable production of 10 l/m.

Unfortunately, our knowledge of the statistical properties of transmissivity
distribution tells us nothing about the spatial distribution of transmissivity or the
actual location of optimum well sites.

COST CONSEQUENCES

Taylor et al. (1999) indicates that the cost of a single well in Ghana ranges
from 2,000 to 4,000 USD. Based on our knowledge of the statistical distribution of
fracture transmissivity, if 100 wells are drilled at an average cost of 3,000 USD, at
least 60,000 USD will be wasted because of poor well locations. For these low cost
wells, analysis of SPOT satellite imagery, TM infrared imagery and fracture trace analysis
using aerial photography is a relatively inexpensive method of well-site location.

Additional, inexpensive field methods, used by AGW scientists, costing about $500 per
well site, can be used to further zero-in on optimum well sites in all areas including
areas of dense vegetation.

The failure rate for wells in Ghana may be tolerable because the wells are of low
capacity and the wells serve a broadly distributed population. A high failure rate
for wells needed to serve large communities and cities cannot be tolerated.